The Inverse Compton Thermostat in Hot Plasmas Near Accreting Black Holes

The hard X-ray spectra of accreting black holes systems are generally well-fit by thermal Comptonization models with temperatures $\sim 100$ keV. We demonstrate why, over many orders of magnitude in heating rate and seed photon supply, hot plasmas radiate primarily by inverse Compton scattering, and find equilibrium temperatures within a factor of a few of 100 keV. We also determine quantitatively the (wide) bounds on heating rate and seed photon supply for which this statement is true. Plasmas in thermal balance in this regime obey two simple scaling laws, one relating the product of temperature and optical depth to the ratio of seed photon luminosity to plasma heating rate $l_s/l_h$, the other relating the spectral index of the output power-law to $l_s/l_h$. Because $\alpha$ is almost independent of everything but $l_s/l_h$, the observed power law index may be used to estimate $l_s/l_h$. In both AGN and stellar black holes, the mean value estimated this way is $l_s/l_h \sim 0.1$. As a corollary, $\Theta \tau_T$ must be $\simeq 0.1$ -- 0.2, depending on plasma geometry.Comment: 26 pages, AASLaTeX, to appear in July 10 Ap.J. Figures available in uuencoded form at ftp://jhufos.pha.jhu.edu/pub/put/jhk/comptfigs.u